Twisted gauge theory model of topological phases in three dimensions
Name
PhysRevB.92.045101.pdf
Size
4.81 MB
Format
Adobe PDF
Checksum (MD5)
3828da66480f199695ef843c7f536ca5
Author(s)
Wan, Yidun
He, Huan
Wang, Juven
Date Issued
July 2015
Journal
Physical Review B
Publisher
American Physical Society
Citation
Wan, Yidun, Juven C. Wang, and Huan He. "Twisted gauge theory model of topological phases in three dimensions." Phys. Rev. B 92, 045101 (July 2015). © 2015 American Physical Society
Version
Final published version
Abstract
We propose an exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasiexcitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the SL(3,Z) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω. Our model fulfills a Hamiltonian extension of the (3+1)-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G. This work is presented to be accessible for a wide range of physicists and mathematicians.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.92.045101
